The 31-year-old announced his retirement from international football last August, but has since returned to Scotland duty and captained his country during Sunday's 1-0 win over Slovenia.
Brown is due to be back in action with Celtic for the start of their Champions League campaign on July 11-12, just over one month after Scotland host England, and he suggested that his club career will take priority over international level.
"We'll see how it goes. It's going to be a hard situation because we are going to be back so early in June," he told Sky Sports News.
"Last year I had the six weeks off, so I need to look after my body as well and see how it is for Celtic. I need to maintain the level and fitness that I have been playing at all season. If I can maintain that as long as I possibly can, you never know."
Scotland's win over Slovenia keeps their World Cup qualification hopes alive with two points now separating them from second-placed Slovakia in Group F.